Vector Field Approximation on Regular Surfaces

The establishment of medium- and long-term ecologically robust forest stocks if of interest for the forestal-structure strategy and the consequential reforestation. The decision on positional stability of different types of trees is among other influences dependent on the modelling of data of the wind field.§The present work deals with the (global and local) modelling of the windfield on the real topography of Rheinland-Pfalz. Thereby the focus is on the construction of a vectorial windfield from low, irregularly distributed data given on a topographical surface. §The developed spline procedure works by means of vectorial (homogeneous, harmonic) polynomials (outer harmonics) which control the oscillation behaviour of the spline interpoland. In the process the characteristic of the spline curvature which defines the energy norm is assumed to be on a sphere inside the Earth interior and not on the Earth`s surface. The numerical advantage of this method arises from the maximum-minimum principle for harmonic functions. The establishment of medium- and long-term ecologically robust forest stocks if of interest for the forestal-structure strategy and the consequential reforestation. The decision on positional stability of different types of trees is among other influences dependent on the modelling of data of the wind field. The present work deals with the (global and local) modelling of the windfield on the real topography of Rheinland-Pfalz. Thereby the focus is on the construction of a vectorial windfield from low, irregularly distributed data given on a topographical surface. The developed spline procedure works by means of vectorial (homogeneous, harmonic) polynomials (outer harmonics) which control the oscillation behaviour of the spline interpoland. In the process the characteristic of the spline curvature which defines the energy norm is assumed to be on a sphere inside the Earth interior and not on the Earth's surface. The numerical advantage of this method arises from the maximum-minimum principle for harmonic functions.